Nonlinear H∞ static output feedback controller design for polynomial systems: An iterative sums of squares approach

An iterative approach for the design of a nonlinear H
_∞
static output feedback controller for polynomial systems is presented in this paper. The proposed controller guarantees the L
₂
-gain of the mapping from exogenous input noise to the controlled output is less than or equal to a prescribed value. The sufficient conditions for the existence of nonlinear H
_∞
static output feedback controller are given in terms of solvability conditions of polynomial matrix inequalities, which are solved using sum of squares decomposition. Numerical examples are provided to demonstrate the validity of applied methods.